Note: Datset donated by Ron Kohavi and Barry Becker, from the article "Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid". Small changes to the dataset have been made, such as removing the
'fnlwgt'feature and records with missing or ill-formatted entries.
Before this data can be used for modeling and application to machine learning algorithms, it must be cleaned, formatted, and structured.
Factor names with special characters, like -, can cause issues, so a cleaning may prove helpful.
Working with categorical variables often involves transforming strings to some other value, frequently 0 or 1 for binomial factors, and {X = x_{0}, x_{1}, ..., x_{n} | 0, 1, .. n} multinomial.
These values may be ordinal (i.e. values with relationships that can be compared as a ranking, e.g. worst, better, best), or nominal (i.e. values indicate a state, e.g. blue, green, yellow).
For training an algorithm, it is useful to separate the label, or dependent variable ($Y$) from the rest of the data training_features, or independent variables ($X$).
The features capital_gain and capital_loss are positively skewed (i.e. have a long tail in the positive direction).
To reduce this skew, a logarithmic transformation, $\tilde x = \ln\left(x\right)$, can be applied. This transformation will reduce the amount of variance and pull the mean closer to the center of the distribution.
Why does this matter: The extreme points may affect the performance of the predictive model.
Why care: We want an easily discernible relationship between the independent and dependent variables; the skew makes that more complicated.
Why DOESN'T this matter: The distribution of the independent variables is not an assumption of most models, but the distribution of the residuals and homoskedasticity of the independent variable, given the independent variables, $E\left(u | x\right) = 0$ where $u = Y - \hat{Y}$ is of linear regression. In this analysis, the dependent variable is categorical (i.e. discrete or non-continuous) and linear regression is not an appropriate model.
| Feature | Skewness | Mean | Variance |
|---|---|---|---|
| Capital Loss | 4.516154 | 88.595418 | 163985.81018 |
| Capital Gain | 11.788611 | 1101.430344 | 56345246.60482 |
| Log Capital Loss | 4.271053 | 0.355489 | 2.54688 |
| Log Capital Gain | 3.082284 | 0.740759 | 6.08362 |